Querying a summary of database - APMD

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66 J Intell Inf Syst (2006) 26: 59–73to be considered as results to a query; there is no need for special operators to deal withthe computation-intensive task of extending criteria. This section deals with all aspects ofselection from the expression and meaning of a query to its matching with summaries.4.1. Expression of a queryThis approach to flexible querying intends to answer questions such as “how are thin materials?”or “how are normal-temperature and soft-hardness materials ?”. In the prototypedeveloped for querying, the questions are expressed using a user-friendly interface that composesthe corresponding query in an SQL-like language. For the two previous questions, thequeries are respectively:Q 1 : SELECT temperature, hardness FROM MATERIALSWHERE thickness IN ("thin")Q 2 : SELECT thickness FROM MATERIALSWHERE temperature IN ("normal") AND hardness IN ("soft")For a more formal expression of a query, let:– S be a set of attributes;– R(S) be the relation whose tuples are summarized;– Q be a query (e.g., Q 1 and Q 2 in the above example);– A i , i ∈{1,...,n} be an attribute appearing in the query (A i ∈ S);– d i, j , j ∈{1,...,m} be a label (or descriptor) of attribute A i , also appearing in the query.In a query, descriptors (like thin, normal or soft in Q 1 and Q 2 ) are called “required characteristics,”and embody the properties that a record must have to be considered as an elementof the answer.A query also defines the attributes for which required characteristics exist. The set of theseinput attributes is denoted by X. The expected answer is a description over a set of otherattributes, denoted by Y . Without further precision, Y is the complement of X relatively toS: X ∪ Y = S and X ∩ Y =∅.Hence a query defines not only a set X of input attributes A i but also, for each attributeA i , the set C Ai of its required characteristics. The set of sets C Ai is denoted by C, as shownin the following example.Example 1. Let Q 1 and Q 2 be the queries stated above. For each query, the sets are:Q 1 : X ={thickness}, Y ={hardness, temperature},C thick ={thin} and C ={C thick }Q 2 : X ={hardness, temperature}, Y ={thickness},C hard ={soft}, C temp ={normal} and C ={C hard , C temp }.When users formulate a question, they expect that all and only the data with the characteristicsthey specify will be returned. The meaning of that question becomes arguable whenmany characteristics are expressed for one attribute or when conditions exist for more thanone attribute.Springer
J Intell Inf Syst (2006) 26: 59–73 67The first case is illustrated by the question “how are materials which are malleable or soft?”.The question is interpreted in a disjunctive manner as “how are materials with hardnessin {malleable, soft}?” and not as “how are materials which hardness is both malleableand soft?”. The equivalent query for the correct interpretation is Q 3 : SELECT thickness,temperature WHERE hardness IN (“malleable”, “soft”), interpreted as the condition hardness= ’malleable’ OR hardness = ’soft’.The second case is illustrated by the question “how are thick compact materials?”. Thequerying process should put forward only data that comply with the characterization on boththickness and hardness. This precludes, for instance, thick soft materials and thin compactmaterials from being selected. The equivalent query for this second question is Q 4 : SELECTtemperature WHERE thickness IN (“thick”) AND hardness IN (“compact”). The conditionof Q 4 is interpreted as thickness = ’thick’ AND hardness = ’compact’.4.2. Evaluation of a queryThis section deals with matching one particular summary against a query to decide whetherit corresponds to that query and can then be considered as a result. The query is transformedinto a logical proposition P used to qualify how one summary relates to the query. P is undera conjunctive form in which all descriptors appear as literals. As a consequence, each set ofdescriptors yields one corresponding clause.Example 2. The query for “how are the materials which are thin or medium-thickness andmoderated or normal-temperature?” is Q 5 : SELECT hardness WHERE thickness IN (“thin”,“medium”) AND temperature IN (“moderated”, “normal”).In Q 5 , X ={thickness, temperature}, C thick ={thin, medium} and C temp ={moderated, normal}. It follows that P 5 = (thin ∨ medium) ∧ (moderated ∨ normal).Let v be a valuation function. The boolean value of P depends on each summary z: aliteral d in P is positively valuated (v(d) = TRUE) if and only if d appears in the intensionalexpression (see Section 3.2) of z. Then v(P(z)) denotes the valuation of proposition P in thecontext of z.Let L Ai (z) be the set of descriptors that appear in z and concern A i . An interpretation of Prelatively to query Q leads to discarding summaries that do not satisfy P. But, as shown in thefollowing example, some summaries that satisfy P might not match the intended semanticsof the query.Example 3. Table 3 shows the characteristics of materials covered by summary z 2 fromTable 2. Suppose z 2 is tested for conformance with a query Q 6 : SELECT temperatureWHERE thickness IN (“thick”, “thin”) AND hardness IN (“soft”, “hard”). P 6 = (thick ∨thin) ∧ (soft ∨ hard) and the function v valuates the variables thin and hard to TRUE as theyTable 3 Example of descriptorcombination Candidate thickness hardnesst b2 thin softt c2 medium hardt e1 thin softz 2 {thin, medium} {soft, hard}Springer
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